Asymptotic properties of the score test for varying dispersion in exponential family nonlinear models

Statistics ◽  
2009 ◽  
Vol 43 (2) ◽  
pp. 105-119 ◽  
Author(s):  
Jin-Guan Lin
Keyword(s):  
Exponential Family ◽  
Nonlinear Models ◽  
Asymptotic Properties ◽  
Score Test ◽  
Varying Dispersion

Testing for Varying Dispersion in Exponential Family Nonlinear Models

1998 ◽  
Vol 50 (2) ◽  
pp. 277-294 ◽  
Author(s):  
Bo-Cheng Wei ◽  
Jian-Qing Shi ◽  
Wing-Kam Fung ◽  
Yue-Qing Hu
Keyword(s):  
Exponential Family ◽  
Nonlinear Models ◽  
Varying Dispersion

scholarly journals SEMIPARAMETRIC ESTIMATION WITH GENERATED COVARIATES

2015 ◽  
Vol 32 (5) ◽  
pp. 1140-1177 ◽  
Author(s):  
Enno Mammen ◽  
Christoph Rothe ◽  
Melanie Schienle
Keyword(s):  
Nonlinear Models ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Control Variable ◽  
Semiparametric Estimation ◽  
Nuisance Parameters ◽  
Infinite Dimensional ◽  
Asymptotically Normal ◽  
Endogenous Covariates ◽  
Nonstandard Problem

We study a general class of semiparametric estimators when the infinite-dimensional nuisance parameters include a conditional expectation function that has been estimated nonparametrically using generated covariates. Such estimators are used frequently to e.g., estimate nonlinear models with endogenous covariates when identification is achieved using control variable techniques. We study the asymptotic properties of estimators in this class, which is a nonstandard problem due to the presence of generated covariates. We give conditions under which estimators are root-nconsistent and asymptotically normal, derive a general formula for the asymptotic variance, and show how to establish validity of the bootstrap.

scholarly journals Bias reduction in exponential family nonlinear models

Biometrika ◽  
2009 ◽  
Vol 96 (4) ◽  
pp. 793-804 ◽  
Author(s):  
I. Kosmidis ◽  
D. Firth
Keyword(s):  
Exponential Family ◽  
Nonlinear Models ◽  
Bias Reduction

scholarly journals Integrated conditional moment test and beyond: when the number of covariates is divergent

Biometrika ◽  
2021 ◽  
Author(s):  
Falong Tan ◽  
Lixing Zhu
Keyword(s):  
Nonlinear Models ◽  
Asymptotic Properties ◽  
Real Data ◽  
Linear Representation ◽  
Wild Bootstrap ◽  
Conditional Moment ◽  
Data Set ◽  
Bootstrap Approximation ◽  
Significance Level ◽  
Fixed Dimension

Summary The classic integrated conditional moment test is a promising method for model checking and its basic idea has been applied to develop several variants. However, in diverging dimension scenarios, the integrated conditional moment test may break down and has completely different limiting properties from those in fixed dimension cases, and the related wild bootstrap approximation would also be invalid. To extend this classic test to diverging dimension settings, we propose a projected adaptive-to-model version of the integrated conditional moment test. We study the asymptotic properties of the new test under both the null and alternative hypotheses to examine its significance level maintenance and its sensitivity to the global and local alternatives that are distinct from the null at the rate n-1/2. The corresponding wild bootstrap approximation can still work for the new test in diverging dimension scenarios. We also derive the consistency and asymptotically linear representation of the least squares estimator of the parameter at the fastest rate of divergence in the literature for nonlinear models. The numerical studies show that the new test can greatly enhance the performance of the integrated conditional moment test in high-dimensional cases. We also apply the test to a real data set for illustration.

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